# For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number.

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For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.

(i) 396   (ii) 2645

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(i) 396 can be factorised as follows.

 2 396 2 198 3 99 3 33 11 11 1

396 = 2 x 2 x 3 x 3 x 11

Here, prime factor 11 does not have its pair. If we divide this number by 11, then the number will become a perfect square. Therefore, 396 has to be divided by 11 to obtain a perfect square.

396 ÷11 = 36 is a perfect square.

36 = 2 x 2 x 3 x 3

∴ √36 = 2 x  3 = 6

(ii) 2645 can be factorised as follows.

 5 2645 23 529 23 23 1

2645 = 5 x 23 x 23

Here, prime factor 5 does not have its pair. If we divide this number by 5, then the number will become a perfect square. Therefore, 2645 has to be divided by 5 to obtain a perfect square.

2645 ÷5 = 529 is a perfect square

529 = 23 x 23

∴ √529 = 23

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